Manchester City and Bayern Munich lead the chase for the 28-year-old superstar who has just a year left on his contract.
Sanchez has so far refused to commit himself to the new deal totalling £300,000-a-week offered by the Gunners.
Chile compatriot and former Real Madrid striker Ivan Zamorano has urged him not to if he wants to win top honours.
Zamorano said: “He’s a guy who has goals and ambitions, they’re fundamental to making a choice. I think he likes to win.
“What he wants, above all, is to win the Champions League, and I don’t think he’ll have that possibility at Arsenal.
“He must know that he will be more useful in a bigger team. But it’s his decision, his personal choice. Whatever happens, Alexis will be at the level he deserves to be and which he must achieve.”
Arsenal will not be in the Champions League next season after failing to make the Premier League’s top four.
They have still, however, managed to land £44million striker Alexandre Lacazette, expected to complete his club-record move from Lyon later this week.